Is (𝛼,𝛾) and (p-𝛾) nuclear transmutation theoretically possible? Some examples would be helpful.

Well... possible and likely enough to ever actually happen can be very different things. Also, we should mention if the reactions you are interested in happen in empty space or with addition of other matter. Alpha particle would have very difficult time becoming a gamma yay on its own... An alpha particle can be absorbed by a nucleus and the resulting nucleus being in excite state can emit a gamma ray; but then you need this "nucleus" so its not just alpha to gamma reaction. In 2011 scientists detected anti-alpha particle https://en.wikipedia.org/wiki/Alpha_particle so if you hit that by alpha you get a barrage of gamma rays. The only way an alpha particle can directly produce a gamma is if the alpha particle was in excited state and it decayed. This paper suggests that an alpha particle can be in an excited sate, hence it can decay via gamma decay, yielding the reaction you are interested in https://www.sciencedirect.com/sdfe/pdf/download/eid/1-s2.0-003191636490736X/first-page-pdf